In known gear machines of the general type to which the invention relates, severe disadvantages have been the expense of their production and the need to maintain precise spacing between the axles of the gears. When producing such a gear machine, one would normally begin with a tooth profile for one of the gears in the shape of a trochoid, a cycloid or a circular arc. The profile of the teeth of the meshing or counter gear is then usually determined empirically as a result of which the making of tools for producing counter gears having the necessary high quality is made very difficult if not impossible. It is particularly problemmatical to develop tools for the generating process since one can operate only with greater dimensional variations or tolerances or else with expenditures which are, economically, not justifiable.
At the present time, special gear teeth of the type requireed are produced in two stages, the first stage being a preliminary shaping with a gear cutting tool (hobbing tool) leaving relatively great tolerances from the final product. The second stage is improvement in the shape and surface quality of the teeth, accomplished by shape grinding. When the degree of overlap between the teeth of the two gears is relatively great, then the spacing between the axles of the gears must be very precisely established in order to avoid disturbances of the gear meshing and mechanically caused noises resulting from manufacturing tolerances. In order to reduce the degree of overlap, the addendum area is frequently shortened which, however, results in additional undesirable dead volume.